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Plot Streamlines with a Density Background
Draw the density of the norm of the vector field as a background.
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StreamDensityPlot[{Cos[x^2 + y], 1 + x - y^2}, {x, -3, 3}, {y, -3, 3},

  ColorFunction -> "RedBlueTones", StreamStyle -> Black, 

 StreamPoints -> Medium, ImageSize -> Large]
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